let-u-n-k-1-n-1-k-ln-n-1-prove-that-u-n-is-convergent-2-let-lim-n-u-n-prove-that-0-lt-lt-1-

Question Number 41345 by maxmathsup by imad last updated on 05/Aug/18

l e t u_{n} = \sum_{k = 1}^{n} \frac{1}{k} - l n (n)

1) p r o v e t h a t (u_{n}) i s c o n v e r g e n t

2) l e t γ = {l i m}_{n \to + \infty} u_{n} p r o v e t h a t 0 < γ < 1

Commented by alex041103 last updated on 06/Aug/18

I s i t \sum_{k = 1}^{n} (\frac{1}{k} - l n (n)) o r (\sum_{k = 1}^{n} \frac{1}{k}) - l n (n) ?

Commented by math khazana by abdo last updated on 07/Aug/18

(\sum_{k = 1}^{n} \frac{1}{k}) - l n (n)